Final answer:
The compass needle would stay oriented toward the magnetic north, and would not change its orientation relative to the airplane while flying due west along the equator, assuming the Earth's magnetic and geographic poles were aligned. In reality, magnetic declination can affect compass readings and should be accounted for in navigation.
Step-by-step explanation:
The original question suggests a scenario where the directional measurement is taken from magnetic north clockwise to the aircraft's nose. However, the body of the question itself seems to deal with the behavior of a compass needle in relation to the Earth's magnetic field while flying due west over the equator. When flying due west along the equator, if the Earth's magnetic north pole and geographic north pole were aligned, a compass would orient its needle perpendicular to the direction of travel, pointing right (north) when crossing the prime meridian due to the interaction with the Earth's magnetic field.
As the plane continues to fly due west, the compass needle would not change orientation significantly relative to the aircraft if the magnetic and geographic poles were perfectly aligned, because the needle aligns with the magnetic field, which encircles the Earth horizontally at the equator and does not vary in direction there. However, in reality, the Earth's magnetic field is not perfectly aligned with its geographic polls, so some degree of variation can be expected as one travels long distances, but this is not relevant in the simplified scenario provided.
Another important point is that magnetic declination - the difference between magnetic north and true north (geographic north) - can affect compass readings depending on one's global position and should be accounted for in precise navigation. Due to the Earth's magnetic field's configuration, magnetic north is effectively the south pole of the theoretical bar magnet representing the Earth.